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Optics Letters

Exact integral solution of saturation and depletion in forward and backward optical fiber Raman amplifiers

Marco Santagiustina

Published Oct 10, 2007• 10 citations
Publisher

Abstract

Exact integral solutions of forward and backward Raman Stokes-pump interaction are presented. They enable one to determine the gain and depletion characteristics of optical Raman amplifiers, as well as a good approximation of the noise figure, without the need of numerically solving the nonlinear boundary value differential equations governing the Raman interaction.

DOI
10.1364/ol.32.003023

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Exact integral solutions of forward and backward Raman Stokes-pump interaction are presented. They enable one to determine the gain and depletion characteristics of optical Raman amplifiers, as well as a good approximation of the noise figure, without the need of numerically solving the nonlinear boundary value differential equations governing the Raman interaction.
The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
Using the semiclassical approach the gain and the noise powers, associated to signal and, generated in optical Raman amplifiers, are estimated for forward and backward configurations. Because it combines a corpuscular approach to a phase-amplitude description of the optical field and of the associated noise, this classical formalism allows to identify, to distinguish and to evaluate the respective noise contributions linked, first, to incident fields, such as input zero-point fluctuations, and relative intensity noise associated to the pump, and to the amplifier itself due to the electron momentum fluctuations at the optical frequency. The contribution of Rayleigh backscattering and pump depletion effects are taken into account. For both configurations, the effects of gain and pump power distribution on noise generation are underlined. The determination of the origin and of the amount of intensity noise at the output constitutes a first step toward the amplification of signal with reduced noise amount in Raman amplifiers.
Using the semiclassical approach the gain and noise powers, associated to signal and, generated in optical Raman amplifiers, are estimated for forward and backward configurations. Because it combines a corpuscular approach to a phase-amplitude description of the optical field and of the associated noise, this classical formalism allows to identify, to distinguish and to evaluate the respective noise contributions linked, first, to incident fields, such as input zero-point fluctuations, and relative intensity noise associated to the pump, and to the amplifier itself due to the electron momentum fluctuations at the optical frequency. The contribution of Rayleigh backscattering and pump depletion effects are taken into account. For both configurations, the effects of gain and pump power distribution on noise generation are underlined. The determination of the origin and of the amount of intensity noise at the output constitutes a first step toward the amplification of signal with reduced noise amount in Raman amplifiers.
Two-beam stimulated Raman scattering with pump and Stokes beams is manifest in both the Raman loss of the pump beam and the Raman gain of the Stokes beam, and it has been used in various label-free bioimaging applications. Here, a three-beam stimulated Raman scattering that involves pump, Stokes, and depletion beams is considered, where two stimulated Raman gain-loss processes are deliberately made to compete with each other. It is shown that the three-beam Raman scattering process can be described by coupled differential equations for the increased numbers of Stokes and depletion beam photons. From approximate solutions of the coupled differential equations and numerical calculation results, it is shown that a highly efficient suppression of the Stokes Raman gain is possible by using an intense depletion beam whose frequency difference from that of the pump beam is identical to another acceptor Raman mode frequency. I anticipate that the present work will provide a theoretical framework for super-resolution stimulated Raman scattering microscopy.
Many applications of forward Raman amplifiers require that transverse spatial amplitude and phase aberrations in the pump beam not be transferred to the phase of the amplified Stokes signal. Detailed one-dimensional depleted-pump calculation are given for two mechanisms that transfer pump aberrations to the Stokes phase. The first is multilongitudinal mode pump fluctuations that vary faster than the coherence time of the Raman transition. The second is saturated dispersion combined with a detuning either due to Raman operation off of line-center or due to the dynamic Stark effect.